I don't understand these significant advantages. No proof ever assumes that there is a unique, algebraically manipulable square root of negative one. There are two such roots, and there is no need to assume anything because the proofs are given in field theory textbooks. Elementary proofs are not necessarily any harder to simplify. A sophicated non-elementary proof might be only 2 lines long, and thus impossible to simplify except by removing reliance on other work. The axiom of choice is not any less rigorous than any other axiom. The whole article is nonsensical. You seem to want to suggest that some proofs are more rigorous than other proofs, but that is just not true at all. [[User:RSchlafly|RSchlafly]] 22:27, 26 August 2009 (EDT) | I don't understand these significant advantages. No proof ever assumes that there is a unique, algebraically manipulable square root of negative one. There are two such roots, and there is no need to assume anything because the proofs are given in field theory textbooks. Elementary proofs are not necessarily any harder to simplify. A sophicated non-elementary proof might be only 2 lines long, and thus impossible to simplify except by removing reliance on other work. The axiom of choice is not any less rigorous than any other axiom. The whole article is nonsensical. You seem to want to suggest that some proofs are more rigorous than other proofs, but that is just not true at all. [[User:RSchlafly|RSchlafly]] 22:27, 26 August 2009 (EDT) |